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In a quadrilateral ABCD, ∠B = 90°. If AD2 = AB2 + BC2 + CD2, Prove that ∠ACD = 90°.

Pythagoras Theorem

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Answer

In right angle triangle ABC,

In a quadrilateral ABCD, ∠B = 90°. If AD^2 = AB^2 + BC^2 + CD^2, Prove that ∠ACD = 90°. Pythagoras Theorem, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

By pythagoras theorem,

AC2 = AB2 + BC2 …….(i)

Given,

AD2 = AB2 + BC2 + CD2

Putting value of AB2 + BC2 from eqn (i) we get,

AD2 = AC2 + CD2

∴ △ACD is a right angled triangle.

In △ACD,

∠ACD = 90° i.e. angle opposite to hypotenuse = 90° (By converse of pythagoras theorem.)

Hence, proved that ∠ACD = 90°.

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